Decoding intelligence via symmetry and asymmetry

Humans use pictures to model the world. The structure of a picture maps to mind space to form a concept. When an internal structure matches the corresponding external structure, an observation functions. Whether effective or not, the observation is self-consistent. In epistemology, people often differ from each other in terms of whether a concept is probabilistic or certain. Based on the effect of the presented IG and pull anti algorithm, we attempt to provide a comprehensive answer to this problem. Using the characters of hidden structures, we explain the difference between the macro and micro levels and the same difference between semantics and probability. In addition, the importance of attention is highlighted through the combination of symmetry and asymmetry included and the mechanism of chaos and collapse revealed in the presented model. Because the subject is involved in the expression of the object, representationalism is not complete. However, people undoubtedly reach a consensus based on the objectivity of the representation. Finally, we suggest that emotions could be used to regulate cognition.


Pattern and certainty
A pattern is essentially an arrangement that is characterized by the order of the elements of which it is made rather than by the intrinsic nature of these elements 12 .Since a pattern is a kind of order, outliers can be viewed as disturbers of the order.That is, if we talk about outliers, we cannot ignore the pattern.The outlier and pattern are one thing; discussing them separately is not ideal.A pattern without outliers is a pure pattern; when we perform outlier detection, we obtain none.This process is also called pattern self-recognition.In essence, pattern recognition can be combined with outlier detection.If we cannot determine this intrinsic structure, we cannot freely perform pattern recognition.
In their first edition 13 , Barnett and Lewis quoted from Ferguson, "It is rather because…, that the loss in the accuracy of the experiment caused by throwing away a couple of good values is small compared to the loss caused by keeping even one bad value.The problem, then, is to introduce some degree of objectivity into the rejection of the outlying observations".The outlier problem tends to be treated as an uncertain problem when it is measured by an objective quantity.After providing the definition of an outlier, Barnett and Lewis concluded that "more fundamentally, the concept of an outlier must be viewed in relative terms" 14 .After carefully studying the nature of outliers, we presented a relatively complete approach 1 in which relativity was emphasized.Concerning the significance of relativity in pattern representation, one chapter 15 provided some arguments.Based on relative references, quantum behavior might be observed consistently 16 .Consistency can be viewed as symmetry, and there is no pattern without breaking.Therefore, we provide the following definitions to show the relation between outliers and patterns.
Definition 1 An outlier is an observation with a degree greater than a threshold in comparison with other observations referred to or associated with a specified pattern.
Definition 2 Pattern recognition is a process of outlier detection based on its ontological spatiotemporal structure.
We cannot see things without measurement; this kind of physical phenomenon deeply impacts our minds.When uncertainty encounters limited measurement, consistency determines appearance.As we could not measure in the continuum, we could not detect outliers in the loop.Therefore, the threshold problem must be solved.Instead of looking for an ad hoc parameter in virtual noise, we should directly introduce the intrinsic parameters of the human sensation system.Web's law states that the ratio of the increment threshold to the background intensity is a constant.This law is suitable for ensuring the certainty of the threshold.
For noise and outliers, additional clarification is needed here.The ambiguity between the two terms was resolved by Abir Smiti 17 , who suggested that noise is of no benefit and should therefore be removed, while outliers can provide both useless and interesting (exceptional) information.Since we employ a holistic approach, we do not specifically distinguish between them.If outliers belong to the pattern, they are one even though they are particularly deviated.Distinguishing is a serial process, while indistinction of a mixed state is a parallel process.Returning to the Yuan's Dos 8 , he actually made a pattern adjustment.Although this approach is appropriate for limited application, it is obvious that it does not consider clearer boundaries at higher dimensions.When we talk about an outlier, we cannot separate it from the specified patterns.The accuracy of the conclusion is up to the completeness of the chosen patterns.

Symmetry and asymmetry for pattern recognition
We begin from a simple example: detecting outliers in the pattern "line".Similarity and offset functions are constructed to evaluate the relationships thereof.The RDD represents the deviation degree to the whole.
Problem 1 Given time series data S1, as shown in Fig. 1, suppose that the data match a linear model and identify outliers.S1 = (3.1,2.9, 2.85, 3, 3.05, 2.9, 3.2, 5.2, 8.5, 5.4, 5.3, 5.1, 3.1, 3.05, 3, 2.99, 3, 3.02, 3.2).By using classic LS regression, we obtain a line y = 3.79-0.001x;by using robust LTS regression, we obtain a line y = 2.907 + 0.007x, as shown in Fig.Although the RDD algorithm has a common form with robust regression, it differs from robust regression that we start from the inside structure of the pattern and emphasize the whole effect, thus resulting in greater balance.Note that the RDD algorithm is the same as robust regression and can be possible with a highest breakdown point (50%).
Relativity means an incomplete state, and using relative deviation to identify the pattern is also incomplete, although it may be effective, necessary and constructive.Therefore, we call the RDD algorithm the incomplete growth (IG) algorithm.Now, we modify our Algorithm 1 to a general form.First, we introduce the definition of view V.
Definition 3 Given time series S, a subseries of S is also a time series where each element is an element of S. We denote e ≺ S when e is a subseries of S.
Definition 4 A view of S, V α , is a set of subseries of S of the same length α , that is, V α = {e | e ≺ S, |e|= α}.

Algorithm 1'
A complete solution for pattern-based outlier detection or outlier-based pattern recognition can be found in our paper 1,15 .The IG algorithm is a kind of interpreting algorithm, which means a kind of symmetry 18 .Regardless of the pattern, if there is no collapse condition, the system will only evolve into an infinite cycle.Therefore, we designed the pull anti 9 , an algorithm for determining the collapse mechanism, which breaks the symmetry.We list the pull anti algorithm as follows.The above algorithm is suitable for univariate data with outliers on the higher side.For convenient use, we also list the algorithms for those data with outliers on two sides here.

Self-expression
The normal and outlier data are similar to those of the figure and ground; once one is determined, the other is also determined.Furthermore, if one pattern is an outlier of another pattern, our solution is widely applicable.To demonstrate the solution clearly, we first consider a simple self-application, which corresponds to the structure representation.
We constructed an expression to pattern "consistency" according to the pull anti algorithm and obtained corresponding RDD data via the IG algorithm.The following comparison of the original data and RDD data through the pull anti algorithm allows us to evaluate the effect of the IG algorithm.We use the BARNETT data as the original one.The consistent principle is described as follows by the definition "consistent sequence".The view used here includes each element.
Definition 5 Given univariate dataset D{d 1 , d 2 , …, d N } in ascending order, for any d i in D, we call www.nature.com/scientificreports/Note: The algorithm uses the nearest neighbor as a reference to construct a consistency sequence and then describes the original elements through the corresponding points on this sequence.
For the RDD series, the corresponding IIR by Pull anti algorithm is calculated.The original data, RDD values and corresponding IIR values are listed in Table 2.The IG algorithm achieved good conversion, and the outlier results were the same.In general, the expression, similarity and offset function determine the result.In other words, what we use determines what we obtain.
We can conclude that if we could find a very precise expression, similarity function or offset function, the RDD series would perfectly reflect the original dataset.In any sense, any pattern recognition problem can be converted to a number problem.The pull anti algorithm splits the numbers.Learning is a process of identifying better expression, similarity and offset functions (hidden or visible).Basically, the IG algorithm can be used for parallel comparisons to confirm what we see.

Alternative expression
In earlier study 15 , computing on probability, or certainty on uncertainty, was proposed to describe intelligent processes.Understanding establishes the relationship between the inside and the outside as well as that between the outside and the outside, and the mind constructs representations and generates understanding.Recently, Douven 19 found that natural color concepts are more readily learned than nonnatural concepts.This is indeed reasonable because construction based on more is always stronger than construction based on less.Gärdenfors et al. 20 presented a framework based on conceptual spaces for reasoning, which provides a more comprehensive understanding of the mechanisms that underlie human reasoning and decision making.They posit that not all mechanisms employed in reasoning can be modeled probabilistically.However, for the conjunction fallacy, the probabilistic DL model presented by Lieto and Pozzato 21 can be shown to be equivalent to their nonmonotonic logic 22 .Therefore, reasoning that does not seem to be based on probability may be caused by preferences.Conceptual spaces provide an intuitive interpretation, and the probability model implies all possibilities 23 .Even if Leslie 24 convincingly showed that there is no satisfactory description of the semantics of Gen, this does not mean that the probability model truly fails.This is very similar to the relationship between the classic world and the quantum world.Moreover, probability can even mean anti-probability if we can correctly express it in the conceptual spaces.We do not believe that these are the two paths of contradiction; they depend on our needs.As the IG algorithm shows, we see what we use.The size of the world determines the depth of insight.Intelligence involves understanding the world through pictures; the full picture constitutes the "universe", and the "universe" in turn affects intelligence.To better interpret the world pictures, we implement the IG algorithm from another perspective.
We use the Barnett data for analysis again.We can randomly choose a reasonable pattern.We consider that the picture describing the data is normal distribution and suppose that all data are just within three-sigma.The "view" could be calculated in this way: For any number, such as 3, its furthest neighbor is found to be 951, as its three standard deviations.The details are as follows.
Vol:.( 1234567890 Note: The algorithm utilizes the farthest point as a reference to construct a statistical model that describes the relationship between other points and itself. The corresponding RDD value and its IIR are listed in Table 3.We find that the result is consistent with that of the direct IIR algorithm.We continue to engage in this scientific endeavor (Table 4).More examples are given in comparison with the direct IIR algorithm.All the results are consistent (the data in bold italic font are outliers).

Discussion
We can continue to perform such experiments to verify the model.If we could not observe inconsistent results after a long test, we would consider ourselves fortunate and agree to accept it as a "standard model".Indeed, this is the process of science.Once we find an inconsistent result, we immediately realize that the model should be modified.The error of a good model should be very small; however, we have probably not reached its underlying foundation.Science involves looking for outliers, which can almost be found.Science is constantly transcending supposed presuppositions, such as absolute space-time and symmetry.This is the deep meaning of the IG algorithm.
Patterns can be recognized because of the uniqueness of the pattern structure, which manifests when intelligence and patterns are unified.The structure-to-pattern involves words similar to semantics.Words might be different, while semantics can be the same.The structure can change, while the pattern is approximate.The IG algorithm is dedicated to symmetry, and pull anti tries to break this symmetry.The bottom layer can be indeterminate, and the top layer must be unambiguous.Therefore, the IG algorithm can be viewed as syntax, and pull anti can be understood as semantics 25 .
While description logics (DLs) are fragments of predicate logic, they are usually represented using syntax based on concepts and roles 26 .A graphic model concerned with the knowledge base can be viewed as a pattern, and possible worlds of the graphic model correspond to semantics; thus, although the pattern is syntactic, the expressions could be semantic.We can observe this in the field of heterogeneous information network (HIN)based recommender systems [27][28][29][30] , which has been increasingly studied in recent years.Meta path-based similarity was first presented for heterogeneous graphs by Sun et al. 31 , who intuitively thought that the semantics underlying different paths imply different similarities.The heterogeneous information network is not a complete information network; thus, the semantics contained in the system are incomplete, which determines the upper bound of the information obtained.Undoubtedly, the structure or pattern represented by paths still implies semantics.The extension of time and space is structural.Although color is conceptual, its expression can be structured more efficiently.The structure shows meaning in relativity, similar to the IG algorithm.The GAT 32 has been widely used as a neural network algorithm, and it is similar to the IG algorithm.The attention mechanism is a semantic transmission that applies the influence of neighbors to itself for comprehensive evaluation.Our paper 15 discusses the holographic characteristics of related algorithms, mining information through integrative relations.The keys of the IG algorithm are equality and observation, and the angles of observation are complementary.Thus, this algorithm can be used on a neural network or not.The actual expression can be different, the spatial dimension can be different, but the interrelationship is the same.The structure contains information, just as none (such as a blind spot) signals that information is missing.Since the heterogeneous information network is not a complete expression of reality (not completely true), the recommendation system is essentially ambiguous, although it is useful.The true value is the most important point of recommendation.Thus, mining disparity is more necessary than mining similarity.Disparity can be measured by inverse similarity; however, they are not symmetrical because the density of space is different, which also influences intelligence.Thus, we mention the derivative intelligence-the inconsistency between reality and truth.If the intelligence structure that matches the structure of the environment is called perception, then attention might be the condition of collapse.The movement of attention 33 in space-time might lead to differences in the algorithm, thus influencing the detail of a representation.Representationalism is macro-level, nonrepresentationalism is microlevel, and combination could produce reality.

Integrative cases and effectivity Longest k-turn subsequence
In this section, we present an example that is more complex than linearity-curves to illustrate the structure of a pattern.The outlier problem of time series data can be described as follows.
Problem 2 Given a sequence S of length N, {d 1 , d 2 , … d N }, which matches the pattern "curve", find outliers.
An example is shown in Fig. 2. www.nature.com/scientificreports/As any curve can be expressed by several ordered sets hinged by several common points, we can develop a dynamic programming algorithm to detect the order of curve type data, which can be traced to the longest increasing subsequence problem 34 .We first define "turn" and then propose the algorithm.Definition 6: Given a curve, except for boundary points, each extremum point is called a "turn point"; the number of extremum points is called turns.We denote the maximum points by the symbol "+" and the minimum points by the symbol "−".If a sequence S has t turns and the 1st one is a maximum/minimum point, then it is denoted by [+/−, t ]. [+, 0] denotes a strictly increasing sequence, and [−, 0 ] denotes a strictly decreasing sequence.
We then introduce the longest k-turn subsequence problem followed by the algorithm.

Algorithm 6 Time series data outliers
Combined with the pull anti algorithm (like an uneven expanding process occurring in a uniform space, some places have increased more than others to attract our attention because the place has gone through an anomaly), Algorithm 6 can be used to solve Problem 2.  5 are not large, which indicates that the deviation from the whole is small.
In previous work 9 , we observed population abnormalities in the roughest way.To better match the structure of the pattern, we use the simplest correction.A sharp decline in the population or a surge in deaths can be captured by the difference between the year and the previous year.In this way, masking and swamping effects need not be considered.When the first outlier is detected, continuous outliers can be checked easily.Although the semantics accompanied by the outliers hidden in the time series data of deaths could also be obtained by uncertain neural networks, it would be better to obtain them by a classic method for efficiency reasons.For this reason, people are more accustomed to reasoning in conceptual space than in probability space.
After sorting the differential sequence, we can use Algorithm 2' for the diagnosis.The comparisons are listed below.Table 6 shows the results of previous work, Table 7

Intelligence and emotion
The intelligence that humans respect is often defined as the ability to understand complex concepts, learn from experience, adapt to the environment and solve problems, which covers many functions, such as perception, memory, reasoning, planning and language understanding.However, since we demonstrated that intelligence was not a mysterious thing, current advances illustrate this point well-artificial intelligence is gradually catching up with humans in all aspects [35][36][37][38][39] .To date, the main criticism of human beings for powerful AI is uncertain thinking because the reasoning of a seemingly probability does not meet human expectations for certainty.However, if we can reflect on the confusions shown in historical research, we may change our minds.First, the Sumerian King List 40 is a confusion that must be faced in the study of ancient history.The selected chronology is as follows.
After the kingship descended from heaven, the kingship was in Eridug.In Eridug, Alulim became king; he ruled for 28,800 years.Alaljar ruled for 36,000 years. 2 kings; they ruled for 64,800 years.
The period of an individual king's reign before and after the flood is in stark contrast.If there is no error in the interpretation of numbers, there must be a change in the law, unless there were different species in ancient times.
If we follow the law of experience and change the interpretation of counting, then language will obviously become an obstacle to the problem.This is not the only difficulty that we have to face; the ancient Egyptian calendar also confuses scholars [41][42][43] , leaving specialists very far from consensus.Historical deterministic events are very similar to the butterfly effect, and an initial flap will cause a storm throughout an entire history.Confirming certainty and preventing fraud has always been the purpose of science [44][45][46] , but a lack of integrity 47,48 is similar to a peer review that shifts from the certainty of content to the certainty of appearance and position.People are unable to achieve identity with many problems, which include not only sociological problems such as history but also problems related to natural sciences such as physics and mathematics.Perhaps what Godel wants to tell us is the necessity of uncertainty, where certainty is nothing more than an illusion that can be repeatedly expressed by perception.In this regard, the late award of the entanglement of quantum and no award of the theory of relativity are the best evidence: certainty should be not only the reality itself but also the time function Whether through representation or non-representation, the object of expression matters.Whether semantic or probability, it is also a method of intelligence.If intelligence is classified according to the worlds, then intelligence must evolve within the universe.Evolutionary intelligence itself is meaningless (imaging AI), so the emotion that is accompanied by intelligence should have meaning.Machine emotion is in the upcoming era and ways in which to express, test and regulate emotion constitute the next problem that must be solved in AI.Emotions are related to ethics, and even academic elites might get out of control on ethical issues [49][50][51] .The incorporation of artificial intelligence into the legal system may be related to the existence of humans.
From a macro point of view, representationalism has clear semantics and is a good choice for intelligent structures, but the attention mechanism 52 at least illustrates its defect.A previous study 53 also indicated that the cortex is involved in reconstruction.Attention reflects the interaction between intelligence and the environment 54 .Humans are susceptible to environmental factors, while AI is not, so it can stably suppress human beings.Intelligence is involved in the process of expression, and expression is not completely static.Representationalism provides commonality and objectivity and is the basis for intelligence to reach consensus, while nonrepresentationalism subjectifies individuality, providing ammunition for conflict.The IG and pull anti algorithms explain patterns from symmetry and asymmetry, which can become the basic structure of intelligence, so that we can visualize the expressed semantics from a macroscopic view and sense the inexpressible probability from a microscopic view.This fusion can be used to make decisions after being directed by emotions.Regardless of whether the "mind" is blank, it can be given different emotions.
The royal Zhou declined, the classics were scattered, and there was academic prosperity in the Spring and Autumn Period and Warring States Period.Other schools of thought were rejected, and only Confucianism was respected, so there was royal dominance and thoughts were imprisoned.Dayu tamed the flood, channeled but not blocked.Shangtang opened the net on three sides and made the best use of everything.If social intelligence is constructed with improper structure, it will distort social norms and limit world pictures, the emotion of the universe will be hurt, the space of concepts will be deformed, the size of granularity will increase and the rhythm of decoupling will be blurred.Each human has the intelligence of a human, a country has the intelligence of a country, and the world has the intelligence of the world.The structure is different, and the performance is different.When emotional factors are added, there will be differences in the interpretation of the structure, and the complexity increases.

Conclusion
This paper aimed to interpret the combined IG and pull anti algorithm from the view of structure.We made contributions in the following aspects.First, we present a definition of an outlier with a certain computability, which allows us to discuss outliers without vagueness.Moreover, we highlight the nature of robust pattern recognition from the view of outliers.Second, we propose an efficient IG algorithm to realize the conversion of patterns.Third, we introduce the "longest k-turn subsequence" to express the pattern of time series data to demonstrate the structure of the pattern.In addition, from the view of evolutionary intelligence, we provide cases for how recognition can be improved by changing the expression of the structure of the pattern.Finally, we discuss the mechanism of the combined algorithm and how to use it to analyze patterns and intelligence: macro-and microexpressions, emotions, limits and pictures.
A pattern is a relationship among elements and is something called a structure.The similarity and offset functions of the IG algorithm are based on observations, i.e., words in representationalism that indicate choices of resolution.A relative mechanism is introduced to process this kind of relation, which completely matches the observation of us to the universe: relativity and quantum 16 .
The combined algorithm might constitute the basis of AI, all intelligent outputs can be verified by this approach and other views equip the brain of AI.The algorithm is hidden, and a visible algorithm is needed for the conscious.Furthermore, as it treats elements on equality in formation, robustness could therefore be guaranteed.
Based on the semantics of the combined algorithm, there is no "objective" pattern.Objectivity can be exploited to express the universe to distinguish inner subjectivity, but even clear semantics are essentially a mapping of probability recognition.The inner order we have determines the external order we can achieve.And the inner order could be connected to emotions, which might be entangled in the universe.Our future work will include emotions, thoughts and ethics.request and with permission of Ministry of Health, Labour and Welfare 1-2-2 Kasumigaseki Chiyoda-ku Tokyo, 100-8916 Japan.Tel : + 81-(0)3-5253-1111 (www-admin@mhlw.go.jp).In addition, part of the data is available at the following URL: https:// www.mhlw.go.jp/ engli sh/ datab ase/ db-hw/ vs_8/ index.html.

Problem 3
Given time series data S of length N, {d 0 , d 1 , …, d N−1 }, with T turns, search for the longest subsequence having T turns by passing the first point p 0 (0, d 0 ).

Algorithm 7 4 .
Output outliers by pull anti algorithm Vol.:(0123456789) Scientific Reports | (2024) 14:12525 | https://doi.org/10.1038/s41598-024-62906-2www.nature.com/scientificreports/In Fig. 2, Points 17, 31, and 25 are confirmed to be different from the others.If they are not being referred to a pattern, it is very difficult to achieve.Notably, the RDD values of 17, 31 and 25 in Table shows the results of this work, and the italics indicate unmatched detections.The time series data include the deaths of 1899-2012 in Japan.Excessive or abnormal deaths can be considered to match certain natural and social disasters, of which the 1918 flu, the 1923 Kanto earthquake (mainly in Tokyo and Kanagawa) and the 1945 war were the three major factors.1920 was the secondary factor associated with the 1918 pandemic, and 1944 and 1946 were the secondary factors associated with 1945.Many recent years (such as 2005-2012) have been included in previous work.Although 1. Based on Definition 1, we present the RDD algorithm.Given a time series data S = d 1 d 2 ……d N , denote point (i,d i ) by p i , and ∠ p j p i p k by ∠ jik (degree).

Table 2 .
and dx is the nearest neighbor of d i in D. BARNETT dataset view1.

Table 4 .
More datasets view2.Significant values are in bolditalic.

Table 6 .
Diseased years diagnosed by original pull anti.

Table 8 .
Comparison of results.